The sum of two numbers is $128$, and their difference is $34$. What are the two numbers?
Solution: Let $x$ be the first number, and let $y$ be the second number. The system of equations is: ${x+y = 128}$ ${x-y = 34}$ Solve for $x$ and $y$ using elimination. Add the top and bottom equations together. $ 2x = 162 $ $ x = \dfrac{162}{2} $ ${x = 81}$ Now that you know ${x = 81}$ , plug it back into $ {x+y = 128}$ to find $y$ ${(81)}{ + y = 128}$ ${y = 47}$ You can also plug ${x = 81}$ into $ {x-y = 34}$ and get the same answer for $y$ ${(81)}{ - y = 34}$ ${y = 47}$ Therefore, the larger number is $81$, and the smaller number is $47$.